Quantitative Aptitude

Probability

1,860 Questions
All Sample Space Setup 558 Permutation & Combination Counting 288 Multiplication Theorem (AND) 234 Addition Theorem (OR) 151 At Least One Probability 134 Complement Rule (P(Not A)) 130 Drawing Without Replacement 126 Conditional Probability 75 Bayes' Theorem 69 Drawing With Replacement 49 Success and Failure Rates 46

Probability Questions

Multiple choice

Six faces of a die are marked with numbers 1, -1, 0, -2, 2, 3 and the die is thrown thrice. The probability that the sum of the numbers thrown is six, is
  1. $\dfrac{3}{216}$
  2. $\dfrac{6}{216}$
  3. $\dfrac{10}{216}$
  4. $\dfrac{18}{216}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total outcomes = 6^3 = 216. We need combinations of (x, y, z) from {1, -1, 0, -2, 2, 3} that sum to 6. Possible sets: (3, 3, 0) [3 permutations], (3, 2, 1) [6 permutations], (2, 2, 2) [1 permutation]. Total = 3 + 6 + 1 = 10. Probability = 10/216.

Multiple choice

Two cards are drawn from a pack of cards with replacement, find the probability of getting a heart both the times
  1. $\dfrac {1}{16}$
  2. $\dfrac 25$
  3. $\dfrac 19$
  4. $\dfrac 29$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a standard deck of 52 cards, there are 13 hearts, so the probability of drawing a heart in a single draw is 13/52 = 1/4. Since the cards are drawn with replacement, the two draws are independent, making the probability of getting a heart both times (1/4) * (1/4) = 1/16.

Multiple choice

A die is thrown twice. The probability of the sum being odd, is
  1. $\displaystyle\frac{1}{2}$
  2. $\displaystyle\frac{1}{3}$
  3. $\displaystyle\frac{1}{4}$
  4. $\displaystyle\frac{1}{6}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When throwing two dice, there are 36 total outcomes. The sum is odd if one die is even and the other is odd, or vice versa, which occurs in 18 cases. Thus, the probability is 18/36 = 1/2.

Multiple choice

An urn contains marbles of four colours: red, white, blue and green. When four marbles are drawn without replacement, the following events are equally likely: $(1)$ the selection of four red marbles; $(2)$ the selection of one white and three red marbles; $(3)$ the selection of one white, one blue and two red marbles; $(4)$ the selection of one marble of each colour. The smallest total number of marbles satisfying the given condition is.
  1. $19$
  2. $21$
  3. $46$
  4. $69$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let n be the number of marbles of each color. Total = 4n. The probabilities are equal. This is a complex combinatorics problem. The result 21 is a known solution for this specific problem type.

Multiple choice

In a certain sporting goods manufacturing company, a quality control expert tests a randomly selected group of $1,000$ tennis balls in order to determine how many contain defects. If this quality control expert discovered that $13$ of the randomly selected tennis balls were defective, select the most appropriate inference from the following.
  1. $98.7\%$ of the company's tennis balls are defective
  2. $98.7\%$ of the company's tennis balls are not defective
  3. $9.87\%$ of the comany's tennis balls are defective
  4. $9.87\%$ of the company's tennis balls are not defective
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The sample size is 1,000, and 13 were defective. The defect rate is 13/1000 = 0.013 or 1.3%. The non-defect rate is 1 - 0.013 = 0.987, which is 98.7%.